Answer:
y=-3/2x+6
Step-by-step explanation:
You can find the slope by taking two points on the graph, and making the one that occurs earlier in the graph (from left to right) the first point (x1, y1) and the one that occurs later in the graph the second point (x2, y2). The equation is m (or slope)=(y2-y1)/(x2-x1). I took the first two points in the table for this. m=(12-18)/-4-(-8)
the double negative on the bottom becomes an addition=> (12-18)/(-4+8)
the top simplifies to be -6 and the bottom simplifies to 4=>-6/4
this fraction can be reduced to -3/2, which is the slope of the graph.
Now, use point slope form (y-y1=m(x-x1)) to find the equation of the graph. Plug any coordinate on the graph in for x1 and y1 here. It should be correct as long as it is a point on the graph, but I am using the point (-8, 18) here.
=>y-18=-3/2(x-(-8))
the double negative in the parentheses becomes a positive=> y-18=-3/2(x+8)
distribute the -3/2 to every term in the parentheses=> y-18=-3/2x-12
add 18 to both sides, cancelling out the -18 on the left side of the equation=>y=-3/2x+6 (-12+18=6 to get 6 for b).
Therefore, the equation is y=-3/2x+6
Answer:
The smallest value of p+q is 11
It happens when p = 6 and q = 5.
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Explanation:
Let's factor 180 in such a way that exactly one factor is a perfect square.
I'll ignore the trivial factor of 1.
Here are the possible factorizations we could go with:
180 = 4*45
180 = 9*20
180 = 36*5
Those factorizations then lead to the following
Then we have
p+q = 2+45 = 47
p+q = 3+20 = 23
p+q = 6+5 = 11
The smallest value of p+q is 11 and it happens when p = 6 and q = 5.
Side note: p+q is smallest when we go with the largest perfect square factor.
Answer:
blue
Step-by-step explanation:
a b c d e
1 2 3 4 5
27-25=2
so b, or blue
Answer:
Difference in scores between his 7th and 8th quizzes = 22
Step-by-step explanation:
Given: Mean score for first 6 quizzes is 33 points. After his 7th quiz his mean score was 32 points. After the 8th quiz the mean was 34.
To find: difference in scores between his 7th and 8th quizzes
Solution:
Mean scores = Total points scored in quizzes ÷ Number of quizzes
So,
Total points scored in quizzes = Mean scores × Number of quizzes
As mean score for first 6 quizzes is 33 points,
Total points scored in 6 quizzes = 6 × 33 = 198
As mean score for first 7 quizzes is 32 points,
Total points scored in 7 quizzes = 7 × 32 = 224
So,
7th score = Total points scored in 7 quizzes - Total points scored in 6 quizzes
= 224 - 198
= 26
As mean score for first 8 quizzes is 34 points,
Total points scored in 8 quizzes = 8 × 34 = 272
So,
8th score = Total points scored in 8 quizzes - Total points scored in 7 quizzes
= 272 - 224
= 48
Therefore,
Difference in scores between his 7th and 8th quizzes = 48 - 26
= 22
Answer:
x = 11
Step-by-step explanation:
(x+5)2 = 32
2x + 10 = 32
2x = 32 - 10
2x = 22
x = 11
